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Properties of Parallel Lines in Geometry

Learn to identify angles formed by two lines and a transversal, including understanding the properties of parallel lines. Explore different types of angles and their relationships. Practice identifying and solving angle measures using algebraic expressions. Improve your geometry skills!

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Properties of Parallel Lines in Geometry

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  1. 3-1 Properties of Parallel LinesM11.B 2.3.11.A Objectives: To identify angles formed by two lines and a transversal To prove and use properties of parallel lines

  2. Vocabulary • A transversal is a line that intersects two coplanar lines at two distinct points. (8 angles are formed) l m t

  3. 4Types of Angles • Alternate interior angles • Same-side interior angles • Corresponding angles • Alternate exterior angles 6 5 3 1 2 4 8 7

  4. Example: Identifying Angles • Same side Interior Angles • Corresponding Angles 1 4 8 5 3 2 6 7

  5. Postulate 3-1: Corresponding Angles • If a transversal intersects two parallel lines, then corresponding angles are congruent. Example: t l m

  6. Alternate Interior/Exterior Angles • If a transversal intersects two parallel lines, then alternate interior angles and the alternate exterior angles are congruent. t a b

  7. Same Side Interior Angles • If a transversal intersects two parallel lines, then same-side interior angles are supplementary. Example:

  8. Find the measure of each missing angle…Justify your answer t l m

  9. Vocabulary - Review • Straight Angle – Angle(s) measure 180° to form a straight angle.

  10. Example: Using algebra to find Angle Measures 2xy (y - 50)

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